Three forces acting on the m₁ are the force of gravity normal reaction by the inclined plane and the tension in the string. The free body diagram for this mass is shown in figure.

Taking the x-axis along incline and y-axis perpendicular it, we have for the x and y components.

x component              m₁ a_x = T – m₁g sinθ                    (I)

y component              0 = N – m₁g cos θ                       (II)

The only forces acting on m₂ are the force of gravity and tension in the string. Free body diagram for mass m₂ is shown in the figure. Taking vertically downward to be the positive y direction we get

m₂ a = m₂ g – T                                                          (III)

(Note : If we choose positive y to be vertically upwards then the acceleration of m₂ will be opposite of m₁)

Solving I and III

If m₂ < m₁ sin θ then m₁ will slide downward.